Question

The degree of the polynomial \( (x^5 + x^2 + 3x) (x^6 + x^5 + x^2 + 1) \) is:

• A. 5
• B. 6
• C. 11
• D. 10

Hint:

When multiplying polynomials, the degree of the product is the sum of the degrees of the individual polynomials. Always check the highest powers of \( x \) in each factor.

Answer 1

The Correct Option is C

Step 1: Recall that the degree of a polynomial is the highest exponent of the variable \( x \) in the expression. The degree of a product of two polynomials is the sum of the degrees of the two polynomials. Step 2: The first polynomial is \( (x^5 + x^2 + 3x) \). The degree of this polynomial is 5, as the highest power of \( x \) is \( x^5 \). Step 3: The second polynomial is \( (x^6 + x^5 + x^2 + 1) \). The degree of this polynomial is 6, as the highest power of \( x \) is \( x^6 \). Step 4: The degree of the product of these two polynomials is the sum of their degrees. Therefore, the degree of the given polynomial is: \[ 5 + 6 = 11. \] Thus, the correct answer is (C).